Water-saturated Granular Medium Research Articles

Dataset of Air Injection into Water-Saturated Granular Media – A Dimensional Meta-Analysis

Dataset of Air Injection into Water-Saturated Granular Media – A Dimensional Meta-Analysis

Force chains, creep and acoustic reflection in marine sediments

Marine sediments are water-saturated granular media. A feature of granular media is that the stress is not uniformly distributed but concentrated in force chains. Several force chains acting in parallel transmit external stresses through the medium. A force chain is a chain of particles through which the external stresses are concentrated and transmitted. Given that the contact stiffness between particles may be approximated as a Maxwell element, i.e. a spring in series with a damper, then the stiffness of any force chain may be modeled as several Maxwell elements in series. It is known that any number of springs and dampers in series may be reduced to just one spring and one damper in series, i.e., one equivalent Maxwell element. Therefore, several force chains in parallel may be modeled as parallel Maxwell elements. However, parallel Maxwell elements may not be reduced to one Maxwell element. The stiffness of a distribution of parallel Maxwell elements falls under the generalized creep model. This model is used to represent the skeletal frame of a larger porous medium model. The inversion of model parameters from the reflection coefficient is explored in the context of a muddy sediment. [Work supported by ONR, Ocean Acoustics Program.]

Numerical and Experimental Study of Wave Propagation in Water-Saturated Granular Media Using Effective Method Theories and a Full-Wave Numerical Simulation

In this article, the detection of an object buried in marine sediments is investigated. Using the results from a series of experiments realized in a tank filled with water and calibrated glass beads, we evaluate the performances for a wide range of the value of the ratio kd of the grain size to the wavelength ( k is the wave number and d is the grain diameter) of three types of prediction tools. The first two prediction tools are based on the definition of an equivalent model. The first tool is based on the well-known Biot–Stoll theory (BM model) while the second tool uses nonperiodic homogenization to define effective velocity and anisotropy maps representing the medium (HM model). The last prediction tool implements a time-domain full-wave numerical method, which takes into account each grain separately (GM model). It is shown that a good agreement between experiments and numerical simulations can be achieved using the BM model for the low kd regime and the HM model for high kd regime.

Model-data comparison of high frequency compressional wave attenuation in water-saturated granular medium with bimodal grain size distribution

Several acoustic models, such as the poro-elastic model, visco-elastic model, and multiple scattering model, have been used for describing the dispersion relation in a porous granular medium. However, these models are based on continuum or scattering theory, and therefore cannot explain the broadband measurements in cases where scattering and non-scattering losses co-exist. Additionally, since the models assume that the porous granular medium consists of grains of identical size (unimodal size distribution), the models does not account for the behavior of wave dispersion in a medium that has a distribution of differing grain sizes. As an alternative approach, this study proposes a new broadband attenuation model that describes the high frequency dispersion relation for the p-wave in the case of elastic grain scatterers existing in the background fluid medium. The broadband model combines the Biot-Stoll plus grain contact squirt and shear flow (BICSQS) model and the quasicrystalline approximation (QCA) multiple scattering model. Additionally, distribution of grain size effect is examined rudimentarily through consideration of bimodal grain size distribution. Through the quantitative analysis of the broadband model and measured data, it is shown that the model can explain the attenuation dependencies of frequency and grain size distribution for a water-saturated granular medium in the frequency range from 350kHz to 1.1MHz. This study can be applied to the high frequency acoustic SONAR modeling and design in the water-saturated environment.

Percus–Yevick radial distribution function calculation for a water-saturated granular medium

This paper presents a practical technique to evaluate the Percus–Yevick (PY) radial distribution function (RDF) for a water-saturated granular medium with a high volume fraction of grains. This is based on the weighted average of the PY RDF׳s recursive formula (Goodwin et al., 1992) and the PY integral equation׳s numerical solution using the filtered fast Fourier transform. In a highly dense medium, the combination of both models produces more accurate and stable results. The error analysis for the volume fraction of scatterers and the distance is given for validation. Finally, using the proposed PY RDF result, we solve an acoustic multiple-scattering equation with quasi-crystalline approximation (QCA) to obtain the effective bulk modulus and attenuation of the water-saturated granular medium, and confirm that our method provides a reasonable result.

High frequency p-wave attenuation dispersion in water-saturated granular medium with bimodal grain size distribution

Compressional wave attenuation in water-saturated granular medium depends on both the frequency and grain size. In recent series of high frequency measurements on porous medium, such as water-saturated glass beads and marine sediments, the effect of grain size distribution on attenuation has been investigated, and a variety of grain size dependence on attenuation has been reported. Particularly, dispersion relation in the granular medium with bimodal grain size distribution is significantly different from that in the medium with unimodal grain size distribution. In this study, two sets of glass beads experiments employing unimodal and bimodal grain size distributions are performed. In order to examine wave propagation phenomenon in the bimodal grains, the attenuation dispersion is represented as a function of three parameters; porosity, volume fraction of scatterers, and Rayleigh parameter kd. Heuristic dispersion model considering scattering phenomenon will also be discussed for comparison with measurements.

Acoustic Rayleigh scattering in water-saturated granular medium with quasicrystalline approximation.

A closed-form solution for the effective wavenumber in a water-saturated medium as a function of the Rayleigh parameter is derived up to the second leading terms in the real part and first leading term in the imaginary part. This is based on the Waterman multiple scattering formulation with the quasicrystalline approximation (QCA) and the Percus-Yevick pair-correlation function. The formula's resultant sound speed and attenuation are compared to the regression relation matching the measurements in the Rayleigh scattering region [Kimura, J. Acoust. Soc. Am. 129(6), 3544-3561 (2011)]. The sound speeds are comparable. However, for the attenuation, it is shown that the QCA result underestimates the measured attenuation while its behavior exhibits similar frequency dependency of f(4).

Penetration of spherical projectiles into wet granular media.

We measure experimentally the penetration depth d of spherical particles into a water-saturated granular medium made of much smaller sand-sized grains. We vary the density, size R, and velocity U of the impacting spheres, and the size δ of the grains in the granular medium. We consider velocities between 7 and 107 m/s, a range not previously addressed, but relevant for impacts produced by volcanic eruptions. We find that d∝R(1/3)δ(1/3)U(2/3). The scaling with velocity is similar to that identified in previous, low-velocity collisions, but it also depends on the size of the grains in the granular medium. We develop a model, consistent with the observed scaling, in which the energy dissipation is dominated by the work required to rearrange grains along a network of force chains in the granular medium.

Determination of grain size distribution in water-saturated granular medium using p-wave attenuation dispersion

P-wave attenuation in the water-saturated granular medium depends on both the frequency and the grain size. In this study, the use of the attenuation dispersion for the determination of grain size distribution in the water-saturated granular medium is discussed. For the dense granular medium, mathematical model considering multiple scattering is used for regression algorithm by fitting model predictions to the measured attenuation data. Inversion of grain size distribution is carried out numerically, and the results are discussed and compared to measured data for the water-saturated glass beads with unimodal and bimodal distributions.

Model-Data Comparison of High Frequency Absorption and Velocity for the Water-Saturated Granular Medium

Dispersion relation for the p-wave sound speed and attenuation has been described by several models based on continuum or scattering theory. As an alternative approach, this study proposes a model describing relation for the p-wave in case of elastic grain scatterers existing in background fluid medium. Dispersion relations are shown as a function of different grain size distribution and Rayleigh parameter . For quantitative analysis of the proposed model, experiments are performed using water-saturated glass beads. Two sets of experiments employing unimodal and bimodal grain size distributions are performed and used for comparison with the current proposed model.

A broadband model for a range of ocean sediments

In the context of the Biot theory of sound propagation in porous media, particularly water-saturated granular media, Yamamoto and Turgut [J. Acoust. Soc. Am. 83(5), 1744–1751, May, 1988] have shown that the pore size distribution can have a profound effect on the frequency dependence of the attenuation of sound. In sandy sediments below the characteristic frequency, the attenuation is predicted to increase as the second power of frequency. In soft sediments, it is found that the rate of increase is closer to the first power. By adjusting the width of the pore size distribution, it is possible to smoothly change from the second power of frequency to the first power, in certain frequency bands. This suggests that pore size distribution may be a critical parameter in the determination of sound attenuation in the seabed. The model predictions are compared to measurements from the Shallow Water 2006 experiment as an illustration. [Work supported by the Office of Naval Research, Ocean Acoustics Program.]

Transport of ARS-labeled hydroxyapatite nanoparticles in saturated granular media is influenced by surface charge variability even in the presence of humic acid

Hydroxyapatite nanoparticle (nHAP) is increasingly being used to remediate soils and water polluted by metals and radionuclides. The transport and retention of Alizarin red S (ARS)-labeled nHAP were investigated in water-saturated granular media. Experiments were carried out over a range of ionic strength (Ic, 0–50mM NaCl) conditions in the presence of 10mgL−1 humic acid. The transport of ARS-nHAP was found to decrease with increasing suspension Ic in part, because of enhanced aggregation and chemical heterogeneity. The retention profiles (RPs) of ARS-nHAP exhibited hyperexponential shapes (a decreasing rate of retention with increasing transport distance) for all test conditions, suggesting that some of the attachment was occurring under unfavorable conditions. Surface charge heterogeneities on the collector surfaces and especially within the ARS-nHAP population were contributing causes for the hyperexponential RPs. Consideration of the effect(s) of Ic in the presence of HA is needed to improve the efficacy of nHAP for scavenging metals and actinides in real soils and groundwater environments.

Undrained shear band in water saturated granular media: A critical revisiting with numerical examples

SUMMARYBy taking into account the continuity of stresses and pore pressure across the boundaries of a shear band, it is theoretically shown that incipient localization may take place in saturated loose contractive sand in the regime of decreasing deviator stress under undrained conditions. The undrained shear band orientation primarily depends on the Poisson's ratio and the dilatancy characteristics of the material. However, under strict isochoric constraint, localization is precluded in dense dilative sand with deviator stress increasing only. If any local volume change takes place with a certain mechanism, undrained shear band would be possible in dense sand, most likely in the regime of decreasing friction angle after the peak friction angle is mobilized. Numerical examples are given to demonstrate the variation of shear band inclinations with void ratios and initial consolidation pressures. Copyright © 2011 John Wiley & Sons, Ltd.

High frequency dispersion model for the water-saturated granular medium

Dispersion relation for the p-wave sound speed and attenuation has been described by several models based on continuum or scattering theory. As an alternative approach, this study proposes a model describing the dispersion relation for the p-wave in case of grain scatterers existing in background porous medium. Dispersion relations are shown as a function of different grain size distribution and Rayleigh parameter ka. For quantitative analysis of the proposed model, experiments are performed using water-saturated glass beads. Two sets of experiments employing unimodal and bimodal grain size distributions are performed and are used for comparison with the current proposed model.

High frequency measurements of sound speed and attenuation in water-saturated glass-beads of varying size

Acoustic measurements of p-wave speed and attenuation were made for water-saturated granular medium, consisting of six kinds of glass-beads with mean grain size ranging from 90 to 875 microm, at frequency range between 400 kHz and 1.1 MHz. Sound speed and attenuation were obtained using the inter-receiver broadband estimation technique. The measured data exhibit various frequency dependencies for the different mean grain sizes, consistent with earlier measurements from other researches. These results reveal that the trend of dispersion relation for the sound speed and attenuation, in the high frequency region, is strongly dependent on the range of Rayleigh parameter kd.

Measurements of sound speed and attenuation for six kinds of water saturated glass beads.

Acoustic measurements of sound speed and attenuation were made in a laboratory water tank containing water saturated granular medium consisting of six kinds of glass beads each with mean grain sizes of 0.090, 0.150, 0.354, 0.507, 0.625, and 0.875 mm for several frequencies extending from 40 kHz to 1 MHz. Cross‐correlation technique and time‐of‐flight technique are used to calculate the sound speed and attenuation of samples. In the presentation, the uncertainties of sediment preparation such as air‐removal, grain packing, and depth‐varying of sediment will be mainly discussed. Also, the observed patterns of the sound speed and attenuation will be presented for the mean grain size, grain size distribution, and frequency.

Nonlinear propagation of laser-generated sound pulses in a water and granular medium

Nonlinear propagation of finite-amplitude acoustic pulse in water and through a sample of water-saturated granular medium is considered. To generate high-intensity acoustic pulses laser generation of sound was used. The region of fluid perturbed by the laser acts as a volume-distributed source. In a fluid with weak light attenuation, a cylindrical source could be formed by a narrow laser beam. The nonlinear distortion of the cylindrical finite-amplitude wave in water is investigated. The measured rate of distortion corresponds to that calculated in the approximation of nonlinear acoustics. In a strongly light-absorbing medium, a wide (compared to the typical sound wavelength) laser beam produces a circular planar source. Such a source produces acoustical pulses of amplitude up to 3 MPa and duration about 1 μs in different fluids. This source was used to investigate the propagation of high-intensity wide frequency band sound signals in a sample of water-saturated cobalt–manganese crust (CMC). Specific acoustical features of the crust such as nonlinear sound pulse distortion and the frequency dependance of attenuation, varying with the amplitude, are considered. Theoretical interpretation of the results is given.

Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium : R. M. Iverson, Mathematical Geology, 25(8), 1993, pp 1027–1048

Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium : R. M. Iverson, Mathematical Geology, 25(8), 1993, pp 1027–1048

Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium

Macroscopic frictional slip in water-saturated granular media occurs commonly during landsliding, surface faulting, and intense bedload transport. A mathematical model of dynamic pore-pressure fluctuations that accompany and influence such sliding is derived here by both inductive and deductive methods'. The inductive derivation shows how the governing differential equations represent the physics of the steadily sliding array of cylindrical fiberglass rods investigated experimentally" by Iverson and LaHusen (1989). The deductive derivation shows how the same equations result from a novel application of Biot's (1956) dynamic mixture theory to macroscopic deformation. The model consists of two linear differential equations and five initial and boundary conditions that govern solid displacements and pore-water pressures. Solid displacements and water pressures are strongly coupled, in part through a boundary condition that ensures mass consereation during irreversible pore deformation that occurs along the bumpy slip surface. Feedback between this deformation and the pore-pressure field may yield complex system responses. The dual derivations of the model help explicate key assumptions. For example, the model requires that the dimensionless parameter B, defined here through normalization of Biot's equations, is much larger than one. This indicates that solid-fluid coupling forces are dominated by viscous rather than inertial effects. A tabulation of physical and kinematic variables for the rod-array experiments of lverson and LaHusen and for various geologic phenomena shows that the model assumptions commonly are satisfied. A subsequent paper will describe model tests against experimental data.

Broadband measurements of acoustic attenuation in water-saturated sands

A method for the measurement of acoustic attenuation in water-saturated granular media as a continuous function of frequency is described. Results for a range of water-saturated sands are presented together with acoustic velocity data and discussed in relation with porosity and grain size variations.